>On a multiple-choice test with four choices per question, someone with no knowledge who guesses randomly will get ~25%.
That would be terrible test design. At my (German) university, most Multiple Choice tests give one point for a correct answer, minus half a point for a wrong answer. That way you expect negative points from people who think they know everything but are no better than random guessing, zero points from somebody who knows nothing, some points from someone who can always narrow it down to two choices.
I guess my point is that you can arbitrarily raise the floor with a bad grading scheme, but there's no inherent reason to do that.